The ongoing controversy over accommodating Muslim women wearing various head coverings is more a debate over religious statements than demonstrating true spirituality. As many Islamic scholars have pointed out, veils are optional and those who choose to wear them do so as a witness of their faith and modesty.
Of course this symbol merely witnesses these things but doesn't actually prove them. The fact that the wearing of veils and coverings in western society draws attention and causes debate actually defeats their stated goal of modest behavior. True modesty deflects attention and lessens interest in oneself. Perhaps in a society where this type of dress has become the norm, the veil can be used without controversy but in western culture it creates the exact opposite effect and negates the statement the wearer desires to make.
As Christians we believe that true spirituality doesn't require special symbols or clothing to be sincere. The epistle of James states it succinctly when it says,
This is pure and undefiled religion in the sight of our God and Father, to visit orphans and widows in their distress, and to keep oneself unstained by the world.
- James 1:27
The witness that James describes here blesses others and proves one's sincerity in religion without drawing attention to self. In addition to this, it does so in such a way that even non-believers can approve and applaud.
In the end, true religion is proven by actions not statements.